We report on a group theory activity in which learners explored dihedral symmetries through a tangible geometric model. This approach has historical roots in the work of Felix Klein's Erlangen Program and his "Elementary Mathematics from an Advanced Standpoint." We situate our study with respect to this history as well as current…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were…

Geometric experience, spatial representation, spatial visualization, understanding the world around us, and developing the ability of spatial reasoning are fundamental aims in the teaching of mathematics. (Freudenthal, 1972) Learning is a process which involves advancing from level to level. In primary school the focus is on the first two levels…

In this paper we focus on creativity needed for geometric tasks designing, visualization of geometric problems and use of ICT. We present some examples of various problems related to tessellations. Altogether 21 students--pre-service teachers participated in our activity within a geometry course at CPU in Nitra, Slovakia. Our attempt was to…

The purpose of this study was to investigate the effects of using dynamic geometry software on preservice mathematics teachers' spatial visualization skills and to determine whether spatial visualization skills can be a predictor of success in learning analytic geometry of space. The study used a quasi-experimental design with a control group.…

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…

Students who struggle with learning mathematics often have difficulties with geometry problem solving, which requires strong visual imagery skills. These difficulties have been correlated with deficiencies in visual working memory. Cognitive psychology has shown that chunking of visual items accommodates students' working memory deficits. This…

Students appear to be able to see number relationships and patterns but have difficulty recognizing the visual properties of shapes, especially if the shapes are in different positions. Their difficulty in the visual and spatial realm is often linked to a lack of drawing experience and possibly undeveloped fine-motor skills. The author, as a…

According to the National Council of Teachers of Mathematics (NCTM) (1989, 2000), students at all levels should be exposed to geometry and measurement topics. Standards documents have identified the importance of primary school students selecting appropriate units for measurements in one- and two-dimensional space (NCTM 1989, 2000). This paper…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

The author recounts experiences introducing a first grade class to the concept of symmetry. The lesson includes activities for developing recognition of objects that have symmetry as well as visualization of both horizontal and vertical lines of symmetry.

Theory and research concerning the development of spatial concepts by young children are discussed. Results of Martin and Kidder are compared with those of Piaget. (SD)

Describes seven spatial abilities related to mathematics including eye-motor coordination, figure-ground perception, perceptual constancy, position-in-space perception, perception of spatial relationships, visual discrimination, and visual memory. Discusses the relationship of the spatial abilities to the study of geometry. Lists 19 references.…

Summarizes findings from research related to spatial abilities. Provided are suggestions for developing spatial abilities. Lists nine references. (YP)